Investigation of Shape Phase Transition in theU(5)-SO(6)Transitional Region by Catastrophe Theory and Critical Exponents of some Quantities

TL;DR

This paper investigates shape phase transitions in Ru and Pd isotopes using catastrophe theory, identifying critical points and analyzing the analogy between quantum and thermodynamic critical exponents.

Contribution

It introduces a novel application of catastrophe theory to analyze the U(5)-SO(6) transition in nuclear isotopes and identifies key candidate isotopes at the E(5) critical point.

Findings

Identification of critical points in Ru and Pd isotopes.

Best candidate isotopes for E(5) critical point.

Establishment of analogy between quantum and thermodynamic critical exponents.

Abstract

In the present paper, by employing the formation of the Catastrophe Theory, the phase transition points for U(5)-SO(6) transitional Hamiltonian, which is defined according to the affineSU(1,1)algebra are investigated. The energy surfaces of the even-even isotopes of Ru and Pd nuclei are considered and special isotopes which are the best candidates for theE(5) critical point are identified. Also, the analogy between the critical exponents of ground-state quantum phase transition and Landau values for the critical exponents of thermodynamic phase transition are described.